Their methodology therefore involves identifying an age profile of the cross-sectional variance. This amounts to disentangling age, time and cohort effects. Since these variables are perfectly collinear (time = cohort + age), Deaton and Paxson normalize the time effects to zero, so that the evolution over time of the cross sectional variances of each cohort is explained only by a combination of age and cohort effects. Without structural and/or out-of-sample information, this normalization is indispensable. Any time trend can be written as combination of age and cohort effects and any age effect can be written as a combination of year and cohort effects.
The normalization is essentially an issue of interpretation when describing average cohort profiles of consumption or wages. In the case at hand, however, the implication of the theory being tested is of a structural relationship between age and the cross sectional variance, and the assumption that all variance trends are explained by cohort and age effects is not particularly appealing.

Our procedure has the advantage of circumventing this issue because it provides a direct test of the central implication of the theory (and of the auxiliary assumptions needed to obtain consistent estimates), namely that the coefficient к in equation (9) equals unity. A second advantage is that it tests a well-defined null hypothesis against which standard inference tools can be applied.

The corresponding drawback, of course, is that we do not confront the theory with any particular shape of the age-profile of the variance of marginal utility. In principle, the shape of this profile allows one to discriminate among competing models, and by assuming certainty equivalence, Deaton and Paxson find a structural relation between the variance of consumption and that of earnings and study how this relation changes over the life-cycle. We are not able to specify such a relation: this is the price we pay for relaxing quadratic utility and using more general preference specifications.